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Explore Biproduct through 4 example sentences from English, with an explanation of the meaning. Ideal for language learners, writers and word enthusiasts.

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Biproduct in a sentence

Related words

Biproduct | Biproducts

Biproduct meaning

An object which is simultaneously the product and the coproduct of some collection of objects.

Using Biproduct

  • The main meaning on this page is: An object which is simultaneously the product and the coproduct of some collection of objects.
  • In the example corpus, biproduct often appears in combinations such as: the biproduct, biproduct exists.

Context around Biproduct

  • Average sentence length in these examples: 18 words
  • Position in the sentence: 1 start, 2 middle, 1 end
  • Sentence types: 4 statements, 0 questions, 0 exclamations

Often before:

finite 1× empty 1×

Often after:

exist 1× exists 1×

Sentence patterns with Biproduct

These short patterns come directly from the example sentences and show how the word is often embedded:

all finite biproduct exist 1× because the biproduct in well 1× if the biproduct a b 1× the empty biproduct exists and 1×

Sentence openings and endings

Common sentence openings:

an additive category 1× properties if the 1× since our category 1×

Common sentence endings:

finite biproduct exist 1× finite biproducts exist 1× the direct sum 1× the zero object 1×

Words around Biproduct

Just before it in the word index:

bipole 3 bipolarity 4 bipolarism 2 bipolar 286 bipods 2 bipod 10

Just after it in the word index:

biproducts 4 bips 2 bipyramid 5 bipyramids 8 bipyridine 2 biqa 4

Similar in corpus frequency:

aaai 6 aani 6 aarne 6 aarya 6 aasb 6 aasen 6

Corpus analysis for Biproduct

  • In this selection, "biproduct" usually appears in the middle of the sentence. The average example has 18 words, and this corpus slice is mostly made up of statements.
  • Around the word, finite, empty, exist and exists stand out and add context to how "biproduct" is used.
  • Recognizable usage signals include all finite biproduct exist and because the biproduct in well. That gives this page its own corpus information beyond isolated example sentences.
  • By corpus frequency, "biproduct" sits close to words such as aaai, aani and aarne, which helps place it inside the broader word index.

Example types with biproduct

The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:

Short example sentences

An additive category is a preadditive category in which all finite biproduct exist. (13 words)

This is because the biproduct in well known preadditive categories like Ab is the direct sum. (16 words)

Since our category C has a zero object, the empty biproduct exists and is isomorphic to the zero object. (19 words)

Longer example sentences

Properties If the biproduct A ⊕ B exists for all pairs of objects A and B in the category C, then all finite biproducts exist. (24 words)

Since our category C has a zero object, the empty biproduct exists and is isomorphic to the zero object. (19 words)

This is because the biproduct in well known preadditive categories like Ab is the direct sum. (16 words)

Example sentences (4)

An additive category is a preadditive category in which all finite biproduct exist.

Properties If the biproduct A ⊕ B exists for all pairs of objects A and B in the category C, then all finite biproducts exist.

Since our category C has a zero object, the empty biproduct exists and is isomorphic to the zero object.

This is because the biproduct in well known preadditive categories like Ab is the direct sum.

Common combinations with biproduct

These word pairs occur most frequently in English texts:

Frequently asked questions

How do you use "biproduct" in a sentence?
An example: "An additive category is a preadditive category in which all finite biproduct exist." This page contains 4 example sentences with the word "biproduct" from authentic English texts.
What does "biproduct" mean?
Biproduct means: An object which is simultaneously the product and the coproduct of some collection of objects.
How many example sentences with "biproduct" are there?
Voorbeeldzinnen.info contains 4 example sentences with "biproduct", drawn from a database of millions of English sentences.